Refractive-diffractive spectrometer

ABSTRACT

A diffraction grating and a prism with the appropriate characteristics are employed to provide a combined dispersive characteristic that is substantially linear over the visible spectrum. Radiation from the grating and prism is collimated by a lens towards a detector array. The grating or a telecentric stop between the grating and prism is placed at a focal point of the lens in a telecentric arrangement so that equal magnification is achieved at the detector array. If the detector array is replaced by a plurality of optical channels, a multiplexer/demultiplexer is obtained. A one or two dimensional detector array may be used for detecting the characteristics of a radiation beam. Alternatively, a one or two dimensional array of optical channels may be employed in a multiplexer or demultiplex arrangement with a single output/input optical channel.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part application of application Ser. No. 11/083,895, filed Mar. 17, 2005; which in turn is a continuation of application Ser. No. 10/723,342, filed Nov. 25, 2003, now abandoned; which in turn is a continuation of application Ser. No. 09/991,038, filed Nov. 21, 2001, now U.S. Pat. No. 6,661,513.

BACKGROUND OF THE INVENTION

This invention relates in general to spectrometers and, in particular, a refractive-diffractive spectrometer.

Spectrometers or spectrophotometers are widely used devices. They are used in digital printers and printing presses. Hand-held spectrometers are used by graphic designers and imaging departments at newspapers, magazines, and copy shops.

In order to analyze the spectro data from images or objects, light from the images or objects is passed through optical elements to a detector, such as a charged coupled device (“CCD”) array. In order to accurately measure the CIE tristimulus values of light sources, images or objects, it would be desirable to accurately resolve all of the wavelength components in the radiation from the light source. Spectrometers resolve such wavelength components by dispersing them at different angles depending on the wavelength. Unfortunately, up to the present time, spectrometers and spectrophotometers do not disperse the different wavelengths linearly. This means that after being dispersed by the spectrometer into the different wavelength components reaching the CCD array, the dispersion of a particular wavelength component is not proportional to the wavelength of the component. For example, if a prism is used in the spectrometer for dispersing the wavelength components of radiation from a source, the angle of refraction of any wavelength component is not proportional to its wavelength.

Radiation from many light sources can have a large number of spectral lines or wavelength components. Therefore, unless the CCD array has the same number of detectors as the number of wavelength components, at least some of the spectral lines or wavelength components of the light source will be directed to positions along the CCD array that does not fall entirely on any particular detector, but may fall partly on one detector and partly on another detector. Since the dispersion of the wavelength components is nonlinear, it cannot be assumed that a linear interpolation of the outputs of the two detectors will yield an accurate measurement of the intensities of such wavelength components. This causes error in measurement. Therefore, to accurately measure the CIE tristimulus values of light sources of filters that have fine spectral detail, spectrometers of the conventional design require higher spectral resolution. However, high quality spectrometers are expensive.

It is therefore desirable to provide improved spectrometers and spectrophotometers in which the above-described disadvantages are avoided.

SUMMARY OF THE INVENTION

This invention is based on the recognition that, by employing two optical elements having a combined dispersive characteristic such that they substantially linearly disperse electromagnetic radiation over at least a portion of an electromagnetic spectrum, the above-described disadvantages of conventional spectrometers and spectrophotometers can be avoided. In the preferred embodiment, a refractive element such as a prism and a diffraction grating may be employed. Preferably, the two optical elements are arranged so that the spectrometer is substantially telecentric; in such event, the spectrometer provides substantially the same magnification at different wavelengths in the spectrum. In other words, radiation energy will be dispersed also linearly across the portion of the electromagnetic spectrum.

Where the combined dispersive characteristic of the two elements is substantially linear, linear interpolation of the type described above would not introduce significant interpolation errors, in contrast to the conventional design of spectrometers. Therefore, even if high resolution CCD arrays are not used, radiation sources, images and objects having a rich spectrum can still be accurately measured. This drastically reduces the cost of the spectrometer.

Instead of actually detecting the different wavelength components, the wavelength components may be directed towards different optical channels in a demultiplexing arrangement. First, the light or radiation source may be an input optical channel carrying radiation of different wavelength components. After passing such wavelength components through the two optical elements, the wavelength components are dispersed substantially linearly. Therefore, irrespective of the wavelengths of the wavelength components in the input optical channel, one can be certain that a particular output channel is carrying a corresponding particular wavelength component. This is not possible if the combined dispersive characteristics of the two optical elements are not substantially linear. The above demultiplexing arrangement is bidirectional. In other words, the separate output channels in the above demultiplexing arrangement can instead become input channels. The wavelength components in such separate input channels, after passing through the two elements, will emerge as a combined beam towards the output channel (the input channel in the demultiplexing arrangement) in a multiplexer arrangement. Again, since the combined dispersive characteristic of the two elements is substantially linear, the different wavelength components will be combined into a single beam by the two elements irrespective of the wavelengths of the different input wavelength components.

The dispersed wavelength components may be directed towards a two dimensional array of detectors for detecting the dispersed electromagnetic radiation dispersed by the at least two elements. Alternatively, the dispersed electromagnetic radiation from an input channel may be directed towards a two dimensional array of optical channels in a demultiplexing arrangement. In such an arrangement, the path of the optical signals can be reversed so that the two dimensional array of optical channels may become input optical channels whereby a two dimensional array of input optical signals may be combined in a multiplexing arrangement and directed towards a single output optical channel.

When one or more of the dispersed wavelength components fall on two detectors, partially on one detector and partially on the other, linear interpolation may be employed to obtain interpolated wavelength components. Preferably, at least one optical value that characterizes radiation may then be derived from the interpolated wavelength components.

The above-described apparatus may also be used for calibrating an optical apparatus. Radiation is passed to at least a first and a second element (such as a refractive element and a diffraction grating) where the at least two elements disperse electromagnetic radiation according to wavelength. The dispersed wavelength components are directed to an array of detectors or optical channels. The dispersed wavelength components are linearly interpolated to obtain information for calibrating the apparatus.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a graphical plot of the natural spectral dispersion of a diffraction grating useful for illustrating the invention.

FIG. 1B is a graphical plot of the natural dispersion of an optical prism useful for illustrating the invention.

FIG. 1C is a graphical plot of the dispersion of the combination of a diffraction grating and a prism.

FIG. 2A is a schematic view of the influx optics portion of a spectrometer to illustrate a preferred embodiment of the invention.

FIG. 2B is a schematic view of the spectrometer section of the embodiment of FIG. 3A.

FIG. 3A is a schematic view of a diffraction grating, a prism and a lens to illustrate one combination of optical elements in the spectrometer to illustrate the invention.

FIG. 3B is a schematic view of a combined grating-prism-lens structure in an embodiment to illustrate still another embodiment of the invention.

FIG. 4 is a schematic view of a filter portion of the spectrometer to illustrate another aspect of the invention.

FIG. 5A is a schematic view illustrating the relative positions of the entrance slit image and of the exit slit or detector to illustrate conceptually the operation of the invention.

FIG. 5B is a graphical plot of the intercepted area of FIG. 5A versus wavelength to illustrate the operation of the invention.

FIG. 6 is a graphical plot of the relative signal obtained by interpolation to illustrate an aspect of the invention.

FIG. 7 is a graphical plot of the percent metameric error versus bandwidth to illustrate the invention.

FIG. 8 is a schematic view of a demultiplexer/multiplexer to illustrate another aspect of the invention.

FIG. 9 is the schematic view of an optical slit, a grating-prism combination and optical sensor or detector array to illustrate the invention.

FIGS. 10A, 10B and 10C are schematic views of a line array of detectors useful for illustrating the invention.

FIG. 11A is a schematic view of a two dimensional array of detectors useful for illustrating the invention.

FIG. 11B is an image of the optical slit of FIG. 9 onto the two dimensional array of detectors of FIG. 11A where the image of the slit is formed by dispersion using the reflective elements and grating combination of FIG. 2B to illustrate an embodiment of the invention.

FIG. 11C is a schematic view of an image of the slit of FIG. 9 formed by conventional optics. A comparison of the image of FIGS. 11B and 11C illustrates the effects of the dispersion optics of FIG. 2B on a two dimensional array of detectors.

FIG. 12 is the simple diagram of a spectrometer connected to a computing device useful for illustrating the invention.

For simplicity in description, identical components are labeled by the same numerals in this application.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1A is a graphical plot of the natural spectral dispersion of a divergent light diffraction grating. As shown in FIG. 1A, a diffraction grating has higher dispersion of longer wavelength components compared to the shorter wavelength components in the visible spectrum. Thus, as shown in FIG. 1A, wavelength components at or near the red end of the spectrum are dispersed by a greater amount compared to wavelength components towards the blue end of the spectrum. FIG. 1B is a graphical plot illustrating the natural dispersion of optical prisms. As shown in FIG. 1B, the dispersion of prisms has the opposite characteristic compared to gratings. Prisms disperse wavelength components at or near the blue end of the visible spectrum by a greater amount compared to other wavelength components. Therefore, by employing both a grating and a prism, the combined dispersive characteristic can be made to be uniform over the entire visible spectrum, as illustrated in FIG. 1C.

The spectrometer of this invention is based on using refraction and a transmissive (or reflective) diffraction grating to produce an efficient and compact spectrometer. The design goal is a linear wavelength dispersion and constant spectral bandwidth. The goals are achieved by using a transmission grating in conjunction with a new form of a lens-prism. A grating, which has high dispersion in the red region of the spectrum, is combined with a lens-prism that has high dispersion in blue spectral region results to produce constant spectral dispersion as shown in FIG. 1C in the same manner just as one would do to achromatize a multi-element lens. The slit magnification is maintained by use of a telecentric stop in the lens-prism. The stop is placed at or near the diffraction grating. The telecentric system maintains a constant F/# across the spectrum and therefore constant slit magnification. The telecentric system has the additional advantage that the detector array is illuminated normal to the array. This configuration minimizes cross talk between array elements. Alternatively, while the rays 30 may remain substantially normal to the detector array, to avoid back-reflection, it may be desirable to slightly tilt the rays or the array so that the rays are at small angles to the normal direction to the array.

With this brief description, the system and the design will be explained in subgroups:

Influx Optics

The influx optics 10 comprises a field lens 12, a slit 14 and a collimator 16 as shown below in FIG. 2A. The field lens is placed just in front of the slit (slit can also be integrated with the lens) to collect light from the target 18 and the slit is placed substantially at a focal point of collimating lens 16. The function of the field lens is to image the collimating lens to the sample area or target 18. With this configuration, all of the light from the sample area 18 that passes through the spectrometer entrance slit also passes through the collimating lens. This minimizes scattered light after the slit since all light leaving the slit will be directed toward the collimating lens.

The width of slit 14 defines the spectral resolution of the system. The slit height is chosen to fill the height of the elements of the detector array in the spectrometer section 20 of FIG. 2B. For a given spectral resolution, the slit width is the product of the focal length of the collimator and angular resolution of the grating of FIG. 2B. Once the spectral resolution and the target area are chosen the collimator dimensions are also defined. In one embodiment, a large slit and a long F/10.0 collimator are used. This makes both the slit and the lens easy to manufacture.

The collimating lens and the following stops define the field of view of the instrument at the target plane. The entrance slit 14 is placed substantially at a focal point of collimating lens 16 so that the collimating lens images the entrance slit to infinity so that the light falling on the grating is collimated (all light rays from a point are parallel). The grating could be illuminated with diverge light. Unfortunately, divergent light passing through the gating produces comatic aberration. The extra aberration would increase the bandwidth of the instrument as a function of wavelength.

The Spectrometer

The spectrometer section 20 has four parts: a grating 22, a telecentric stop 24, a lens-prism 26 and detector array 28, such as a CCD array. These elements are shown in FIG. 2B. The collimated light from the front section 10 passes through and diffracted, or is reflected and diffracted, by the grating and is dispersed into its spectral components as shown in FIG. 2B. These rays are further dispersed by the first surface of the lens-prism element. In one embodiment, the grating is ruled at 600 lines/mm. The grating frequency and the prism angle are part of the design optimization. The lens-prism comprises a prism portion 26 a and a lens portion 26 b. The last variable in the optimization is the choice of which wavelength will strike normal to the second face 26′ of the prism portion. It is this ray (the center ray 30′ in FIG. 2) that is the optical axis of lens portion 26 b that makes up the second face of the lens-prism. The grating frequency, prism angle and wavelength of the chief ray (optical axis) are chosen to produce a system with linear spectral dispersion. Any one of the commonly used optical component design programs may be used to provide a precise optical design for a system with linear spectral dispersion given the above inputs (grating frequency etc.) so that it is not necessary to describe the process in detail.

In one embodiment, the grating frequency is targeted to be in the range of 500 to 600 lines/mm. The frequency is kept low to minimize polarization efficiency differences. At higher frequencies polarization scramblers would be required to compensate for these polarization differences. The grating is blazed for the first order. The blaze angle is determined by the spectral sensitivity of the system. The wavelength of the maximum efficiency is placed where the system has the least sensitivity. In general the optimum solution is to have the same signal strength from each portion of the spectrum when reading a perfect white reference.

The lens-prism 26 is designed so that the first or higher order diffracted light is collimated and transmitted by the grating 22 and focused on the detector array 28. The length of the prism is determined by the focal length of the final lens surface of lens portion 26 b. The face 26″ of the prism portion next to the grating is approximately at the infinity focus of the Lens-Prism. As shown in FIG. 2B, rays 30 of light leaving a point near the grating leave the final lens in a collimated state (parallel). This is the telecentric condition. To achieve such condition, the telecentric stop 24 is located at or substantially at a focal point of the lens portion 26 b. If no stop 24 is employed, the grating 22 is located at or substantially at a focal point of the lens portion 26 b. This enables substantially equal magnification of all wavelength components in all the rays 30. Surface 26″ may be aspheric as shown in dotted line in FIG. 2B to compensate for geometric aberration introduced by the collimating lens 16 of FIG. 2A.

The detector array 28 is positioned to be in focus at each wavelength and substantially perpendicular to the telecentric rays leaving the final lens surface of lens portion 26 b. This position of the array 28 minimizes cross talk between elements and assures constant slit magnification and therefore constant spectral bandwidth at every detector site in the array.

While in the preferred embodiment, a lens-prism 26 is employed, it is also possible to use a separate prism and a separate lens instead, as illustrated in FIG. 3A. In such event, the telecentric stop 24 is placed at a focal point of lens 34. Where no stop 24 is used, grating 22 is placed at a focal point of lens 34. In the same manner as illustrated above in reference to FIG. 2A, 2B, grating 22 of FIG. 3A may act as a transmissive or reflective grating. In other words, light (preferably collimated) from the target may pass through and diffracted by grating 22 and proceed towards prism 32 and lens 34, or is reflected and diffracted by the grating. In any event, the first or higher order diffraction passes through prism 32 and lens 34 and is incident on a detector array such as array 28 (not shown). In still another arrangement, all three elements: the grating, the prism and the lens may be combined into a single optical element 40 as shown in FIG. 3B. In such event, the grating surface 40′ is located substantially at a focal point of the lens portion 40″ of the element.

FIG. 4 is a schematic view illustrating a filter placed in front of the detector array 28 to further reduce cross-talk in the spectrometer of this invention. As shown in FIG. 4, the rays (such as rays 30 of FIG. 2B) that are directed towards the detector array are first passed through corresponding filter elements 50 before the filtered rays are then directed towards the detector array 28. While only seven filters 50 are shown in FIG. 4, comprising blue, blue-green, green, yellow, orange, red-orange and red filters, it will be understood that more or fewer filters may be employed, which is within the scope of the invention.

Explained below is the reason why the new Grating-Prism-Lens (GPL) Spectrometer of this invention has the calorimetric accuracy of a spectrometer with a much smaller bandwidth. A 1 nm bandwidth conventional system is compared to a 10 nm GPL system.

The GPL spectrometer (such as system 20 of FIG. 2B) has been designed to have two unique features. The first is that by using a prism combined with a grating, the dispersion of the system is made linear or substantially linear over the visual wavelength region of 400 nm to 700 nm. By using a prism combined with a grating, the dispersion of the system can also be made linear or substantially linear over a portion of the spectrum that includes wavelengths in the infrared or ultraviolet range. Thus, the spacing between 10 nm samples occurs at equal distances in the image plane. Second, the use of the telecentric condition produces a system that has constant magnification of the slit for all wavelengths. Therefore, an array detector with 10 nm spacing between detectors will be just filled with light by a line source that is at the center wavelength of the detector.

FIG. 5A illustrates how the image of the entrance slits, from wavelengths differing from the center wavelength of the detector element, move across the array element. The detector element acts as the exit slit of the system. FIG. 5A shows how much of the light is intercepted for each of the line spectra. The images 14′ of the slit 14 of FIG. 2B on the exit slit (detector) are shown for wavelength differences of −6 nm, −3 nm, 0.0 nm, 3 nm and 6 nm. The amount of energy intercepted by the exit slit is directly proportional to the difference between the center wavelength of the exit slit position and the wavelength of the entering light. Therefore, if the wavelength difference is zero, all the light from the entrance slit will fall on the exit slit. As is shown in the plot on FIG. 5B, the amount of light intercepted by the exit slit is a linear function of the difference between wavelengths. The amount of light intercepted by the exit slit is zero for differences of 10 nm or greater. The amount of light falling on a detector is a triangular function of the difference in wavelength between the center wavelength and the wavelength of the entering light.

The GPL is different from other spectrometer configurations. All others have some form of uncorrected dispersion. As such, none of them exhibit the natural interpolation abilities of the GPL spectrometer. All other spectrometers require higher spectral resolution to accurately measure the CIE tristimulus values of source or filters that have fine spectral detail. The GPL spectrometer can determine the CIE tristimulus values of line spectra without the need to resolve the line spectra. The next section illustrates the ability of the GPL system.

GPL CIE Tristimulus Determination

Spectrometers in use today require a resolution of 1 nm to determine the tristimulus values of sources that have line spectra included in a continuum spectrum. Fluorescent lamps and monitor phosphors are good examples of problem sources that normally require high spectral resolution. The GPL spectrometer has the ability of obtaining accurate CIE tristimulus values without the need to resolve the spectral lines. Since all radiation is just the sum of an infinite number of spectral line sources, the GPL will yield accurate tristimulus values for all light distributions. The following discourse will illustrate the ability of the GPL system to produce exact CIE tristimulus values for an infinitesimal width spectral line source.

FIG. 6 shows the spectral response functions of two adjacent detectors in an array of detectors. An arbitrary and perfect line source is received by the GPL system that has a wavelength that is between these detectors. The source wavelength is assumed to be placed at a distance α times the spectral distance between the adjacent detectors.

A perfect spectrometer with a small enough bandwidth is assumed to resolve the source given above. One would then know the exact center wavelength of the source and the energy of the source, Es. The tristimulus value of the source would be computed by linear interpolation. The known source wavelength lies between two wavelengths where the CIE color mixing functions have been tabulated. The tristimulus value is given by linear interpolation: T=M1*Es*(1−α)+M2*Es*α  (1) where M1 is the color mixing function at the lower wavelength and M2 at the upper wavelength. The source wavelength lays a proportionate distance α from the lower wavelength.

FIG. 6 shows how the source is seen by the GPL spectrometer. The original energy passing through the entrance slit falls on both detectors. Detector 1 receives E1 amount of energy and detector 2 receives E2. The tristimulus value would be calculated as follows: T=W1*E1+W2*E2  (2) From FIG. 6, one can see that the triangular band pass of GPL devise splits the energy, Es, as follows: E1=Es*(1−α)  (3) and E2=Es*α  (4) Now if equations 3 and 4 are substituted for E1 and E2 in equation 2, we obtain: T=W1*Es*(1−α)+W2*Es*α  (5)

This is the same result obtained by the spectrometer with infinite resolution. Therefore, if the use of the spectrometer is to determine the tristimulus values of a source, the GPL spectrometer will give the proper result. If the purpose is to accurately resolve the spectral components of the source, then the broad band GPL is not the appropriate tool.

Bandwidth Considerations

The final question in the design of the GPL device is the wavelength spacing of the samples. The choice was made to use 10 nm spacing. This choice is a compromise between accuracy and sensitivity. The sensitivity of the instrument increases with increase of bandwidth. Unfortunately the metamerism error in the computation of tristimulus values increases with spectral bandwidth. Triangular filtering a 1 nm table of color mixing functions to a 3, 10 and 20 nm bandwidth simulated the optical actions of each spectrometer. The metameric error is calculated by subtracting the linear interpolated data from the true 1 nm color mixing functions. FIG. 7 displays the increase of standard deviation of metameric error as a function of spectral bandwidth. A spectral resolution of 10 nm is chosen as optimum compromise between sensitivity and metameric error. Note that the error difference between a 3 nm and a 10 nm bandwidth is small as compared with an instrument with a 20 nm bandwidth.

The GPL spectrometer has been designed to have linear dispersion and constant slit magnification over the spectral region of 400 to 700 nm. As a result the instrument can measure the CIE Tristimulus values of sources that contain very spiky spectral components. An analysis is made of the metameric error in the weighting functions as a result of using the triangular spectral band pass as an interpolator. It is found that 10 nm was the upper limit of the allowed spectral band pass to limit metameric error to a value of 0.001639 RMS of the true value of the color mixing functions. This value is only slightly larger that a system with a 3 nm bandwidth.

Multiplexer/Demultiplexer

The above-described diffraction grating and prism may also be used in optical multiplexers and demultiplexers as illustrated in FIG. 8. Thus, in reference to FIGS. 2A and 2B, if the radiation or light collected by field lens 12 originates from an optical channel such as an optical fiber, such radiation is collected by lens 12 in the same manner as that described above. Radiation from collimator 16 then undergoes diffraction and other optical operations in FIG. 2B, except that instead of being detected by a detector array 28, each of the rays 30 is collected by a corresponding output optical channel. In other words, the different wavelength components from an input optical channel is dispersed into its different wavelength components where each wavelength component is then collected by a corresponding output optical channel, thereby functioning as an optical demultiplexer.

Thus, as shown in FIG. 8, each of the three arrows 102 is an input optical channel. For each input optical channel 102, there is a corresponding optical system comprising lens 12, slit 14, collimator 16, grating 22, stop 24, lens-prism 26 and the separated wavelength components are collected by a plurality of three output optical channels. While only three output optical channels 104 are shown collecting the wavelength components originating from each input optical channel 102, fewer or more output optical channels may be employed and is within the scope of the invention. Thus, output optical channels 104′ are used to collect rays 30 that originate from input optical channel 102′, and direct these optical signals to corresponding receivers (not shown). The same advantages of linear dispersion and equal magnification can advantageously be used in the demultiplexer 100. Since the dispersion is linear, it would be easy to identify the spacing and location of the output optical channels 104, if the expected wavelengths of the input radiation is known. It would then be much simpler to design the demultiplexer 100. Since system 100 provides substantially the same magnification for all wavelength components, there would be little or no distortion or unequal reduction of intensity of the wavelength components between the different wavelength components in the different output channels.

As shown in FIG. 8, where the input and output optical channels are optical fibers, a GRIN lens (not shown) may be used as an optical interface for each of the optical channels in FIG. 8.

The passage of radiation in system 100 is bidirectional. This means that system 100 may also function as a multiplexer by converting each of the input optical channels 102 into output optical channels and the output optical channels 104 into input optical channels. In such event, the different wavelength components carried by the input optical channels 104′ would then be combined and directed towards the output optical channel 102′ in such multiplexer. Again, if the optical channels are optical fibers, GRIN lenses may be employed as optical interfaces.

FIG. 9 is a schematic view of the optical arrangement of FIG. 2B, useful for illustrating the invention. As shown in FIG. 9, the input optical beam is dispersed into a dispersed beam 30 comprising a number of different wavelength components. These wavelength components are detected by different detectors in the array 28 where the wavelength of the components are dispersed along the direction 50 and labeled k.

FIG. 10A is a schematic view of a linear array of detectors 28 which may be used to detect the various wavelength components in beam 30. As shown in FIG. 10A, each detector has a certain width along the direction 50 and a certain height in the direction perpendicular to direction 50. FIG. 10B illustrates detector array 28 where the wavelength components of beam 30 are projected onto the detector array. Viewed from a different point of view, an image of the slit 14 is imaged onto detector array 28. As will be observed on FIG. 10B, the image of the slit 14 is substantially rectangular; the wavelength components are evenly spread along direction 50 due to the telecentricity of the optical components 22, 26. In contrast, if conventional spectrometer optics are used instead of components 22 and 24 for projecting the image of slit 14 onto detector array 24, the result is illustrated in FIG. 10C. Since conventional spectrometers are not telecentric, the wavelength components are not evenly spread so that linear interpolation may not be used for ascertaining the optical characteristics of the radiation beam.

For some applications, it may be desirable to increase the signal-to-noise ratio in the spectrometer. For this purpose, a two dimensional array of detectors such as array 100 of FIG. 11A may be used instead of the linear array 28, such as in FIG. 9. The two dimensional detector array 100 may comprise detectors arranged along two orthogonal directions: 50 and 102, where direction 50 is also the direction of dispersion caused by optical elements. The detectors in array 100 arranged along direction 50 may be referred to as rows of detectors and those along the direction 102 may be referred to as columns of detectors. Thus each wavelength component from beam 30 may be detected by one or two columns in detector array 100 instead of one or two detectors as in the case of array 28. The intensity of the wavelength component detected by detectors increases linearly with the number of detectors whereas noise increases only as the square root of the number of detectors. Thus by using a larger number of detectors (such as groups arranged in columns of detectors rather than single detectors along direction 102), the use of the two dimensional detector array 100 increases the signal-to-noise ratio.

As in the case of a spectrometer using a line detector array, linear interpolation may be used in the case of a two dimensional detector array only when the system is telecentric. This is illustrated in FIGS. 11B and 11C. FIG. 11B is a view of an image of the slit 14 on the two dimensional array 100 formed by optical elements combination 22 and 26. FIG. 11C is an image of slit 14 projected on detector array 100 when conventional spectrometer optics is used. As will be apparent from the comparison of the two images in FIGS. 11B and 11C, unless the type of optics used meets the above conditions (linear dispersion and telecentricity), the image of the slit will be distorted, sometimes severely, so that the above-described improved signal-to-noise ratio may not be achieved.

Instead of using grating 22 and prism 26 in FIG. 2B in combination with a two dimensional detector array, other types of spectrometer optics described above may be used, such as that shown in FIG. 3A or FIG. 3B. Such and other variations are within the scope of the invention. As will be observed from the above scheme, each wavelength component of the radiation dispersed is detected by a group of detectors, such as one or two columns of detectors, in FIG. 11B. Where the wavelength component falls onto a single column of detectors in array 100, such column of detectors then is the group of detectors detecting such component. Where the wavelength component falls onto two adjacent columns of detector array 100, the two adjacent columns of detectors then form the group of detectors detecting such components. As will be observed from FIG. 11B, the image of the slit 14 is substantially rectangular; the wavelength components are evenly spread along direction 50 due to the telecentricity of the optical components 22, 26.

In the same vein, a two dimensional array of optical channels may be used for receiving the dispersed beam 30, analogous to the arrangement shown in FIG. 8. In such alternative demultiplexer arrangement, the optical configuration of FIG. 8 need to be modified only slightly to illustrate such configuration. First FIG. 8 may be modified by eliminating two of the input beams, thereby resulting in a single input beam, such as input beam 102. The different wavelength components of the dispersed beam are then directed to a two dimensional array of output optical channels, such as the nine optical channels 104 shown in FIG. 8. It will be noted that the optical output channels that are spaced apart from each other along the direction of dispersion by means of the spectrometer in FIG. 2B, 3A or 3B will receive wavelength components of different wavelengths, whereas the optical channels dispersed in a direction perpendicular or to the dispersion direction will receive wavelength components of substantially the same wavelength. If the direction of the optical signals in the channels is reversed, the arrangement becomes a multiplexer arrangement.

The process of linear interpolation is described above. In one instance, for example, the interpolation of a wavelength component falling onto two adjacent detectors may be linearly interpolated to obtain an interpolated wavelength component in accordance with equations 1-4. Other wavelength components falling onto two adjacent detectors may be linearly interpolated in a similar manner. The weighting factors such as M1, M2 and W1 and W2 are readily available from published tables such as those of colorimetry. Summation of wavelength components so interpolated can yield tristimulus values, or other types of values such as Agtron or PAR values. The scheme of the present application may be used to determine the optical characteristics of radiation, however originated, by deriving at least one optical value that characterizes such radiation. These values may be computed (linear interpolation, summation etc.) by means of an electronic device 120, such as a computer as shown in FIG. 12. As shown in FIG. 12, computer 120 receives the signals representing the intensities of the detected wavelength components from device 20, where the detector array therein can be a one or two dimension detector array.

While the invention has been described above by reference to various embodiments, it will be understood that changes and modifications may be made without departing from the scope of the invention, which is to be defined only by the appended claims and their equivalent. For example, while it is preferred to employ a refractive element and a grating so that their combined dispersion is substantially linear, it may be adequate for some applications where the combined dispersion over at least a portion of an electromagnetic spectrum is not linear, but nevertheless more even than by only one of the two elements. All references referred to herein are incorporated by reference in their entireties. 

1. An apparatus, comprising: at least a first and a second element that disperse electromagnetic radiation according to wavelength, said at least two elements having a combined dispersive characteristic such that they substantially linearly disperse the electromagnetic radiation over at least a portion of an electromagnetic spectrum, wherein said at least two elements are arranged so that the apparatus is substantially telecentric; and a two dimensional array of detectors detecting the electromagnetic radiation dispersed by said at least two elements.
 2. The apparatus of claim 1, wherein a group of detectors of said array detects electromagnetic radiation of a corresponding wavelength range in the spectrum.
 3. The apparatus of claim 1, wherein said array comprises a plurality of groups of detectors, each group detecting electromagnetic radiation of a corresponding wavelength range in a spectrum.
 4. The apparatus of claim 3, wherein said plurality of groups of detectors contain substantially the same number of detectors.
 5. The apparatus of claim 4, wherein when the array is aligned with the electromagnetic radiation dispersed along a first direction, each group of detectors lies along a second direction substantially perpendicular to the first direction.
 6. The apparatus of claim 1, further comprising an entrance slit between the two elements and the array, wherein when the array is aligned with the electromagnetic radiation that is dispersed along a first direction, an image of the slit is formed on said array of detectors so that said image has substantially constant height along a second direction perpendicular to the first direction.
 7. The apparatus of claim 1, said at least two elements including a refractive element and a grating.
 8. The apparatus of claim 7, wherein said at least two elements include a prism.
 9. The apparatus of claim 1, further comprising an entrance slit between the two elements and the array wherein said at least two elements convey electromagnetic radiation from the entrance slit to the detector array and said apparatus provides substantially the same magnification of the entrance slit at the detector array at different wavelengths in the spectrum.
 10. The apparatus of claim 1, further comprising a lens, said at least two elements including a grating placed substantially at a focal point of the lens that focuses the electromagnetic radiation from the grating to the detector array.
 11. The apparatus of claim 1, said at least two elements comprising a lens component, and a grating placed substantially at a focal point of the lens component that conveys the electromagnetic radiation from the grating to the detector.
 12. The apparatus of claim 11, said at least two elements comprising a prism integral with the lens component.
 13. The apparatus of claim 1, further comprising a lens, said at least two elements including a prism and a grating, wherein the prism, lens and grating are separate components.
 14. The apparatus of claim 1, further comprising a lens, said at least two elements including a prism and a grating, wherein any two or more of the prism, lens and grating are combined to form a unitary single optical component.
 15. The apparatus of claim 14, wherein the prism, lens and grating are combined to form a unitary single optical component.
 16. The apparatus of claim 1, said at least two elements including a prism, a grating and a lens component integral with the prism.
 17. The apparatus of claim 1, said at least two elements including a transmissive or reflective grating.
 18. The apparatus of claim 1, said at least two elements comprising a prism having a surface receiving the electromagnetic radiation from a collimating lens, said surface being aspheric to compensate for geometric aberration introduced by the collimating lens.
 19. The apparatus of claim 1, wherein said at least two elements are integral with one another to form a single optical member.
 20. An optical apparatus, comprising: at least a first and a second element that disperse electromagnetic radiation according to wavelength, said at least two elements having a combined dispersive characteristic such that they substantially linearly disperse the electromagnetic radiation over at least a portion of an electromagnetic spectrum, wherein said at least two elements are arranged so that the apparatus is substantially telecentric; and a two dimensional array of input/output optical channels conveying electromagnetic radiation signals to or from the at least two elements, said at least two elements multiplexing or demultiplexing the electromagnetic radiation signals.
 21. The apparatus of claim 20, wherein a group of optical channels of said array conveys electromagnetic radiation of a corresponding wavelength range in a spectrum.
 22. The apparatus of claim 20, wherein said array comprises a plurality of groups of optical channels, each group conveying electromagnetic radiation of a corresponding wavelength range in a spectrum.
 23. The apparatus of claim 22, wherein said plurality of groups of optical channels contain substantially the same number of optical channels.
 24. The apparatus of claim 23, wherein when the array is aligned with the electromagnetic radiation dispersed along a first direction, each group of optical channels lies along a second direction substantially perpendicular to the first direction.
 25. The apparatus of claim 20, further comprising an entrance slit between the two elements and the array, wherein when the array is aligned with the electromagnetic radiation that is dispersed along a first direction, an image of the slit is formed on said array of optical channels so that said image has substantially constant height along a second direction perpendicular to the first direction.
 26. A method for determining optical characteristics of radiation, comprising: passing said radiation to an apparatus comprising at least a first and a second element that disperse electromagnetic radiation according to wavelength, said at least two elements having a combined dispersive characteristic such that they substantially linearly disperse the electromagnetic radiation over at least a portion of an electromagnetic spectrum, wherein said at least two elements are arranged so that the apparatus is substantially telecentric; detecting wavelength components of the radiation dispersed by the apparatus; linearly interpolating the detected wavelength components to obtain interpolated wavelength components; and deriving from the interpolated wavelength components at least one optical value that characterizes the radiation.
 27. The method of claim 26, said linear interpolating comprising obtaining weighting values from a reference.
 28. The method of claim 27, wherein said detecting detects by means of a two dimensional detector array comprising a plurality of groups of detectors, each group detecting electromagnetic radiation of a corresponding wavelength range in a spectrum, and wherein said interpolating interpolates outputs of groups of detectors of the array.
 29. The method of claim 28, further comprising aligning the array with the dispersed radiation.
 30. The method of claim 26, said at least one optical value comprising a tristimulus, Agtron or PAR value of the radiation.
 31. The method of claim 30, said deriving comprising summing the interpolated wavelength components to obtain said tristimulus, Agtron or PAR value of the radiation.
 32. A method for calibrating an optical apparatus comprising at least a first and a second element and an array detectors or optical channels, said at least two elements having a combined dispersive characteristic such that they substantially linearly disperse the electromagnetic radiation over at least a portion of an electromagnetic spectrum, wherein said at least two elements are arranged so that the apparatus is substantially telecentric, said method comprising: passing radiation to said at least a first and a second element that disperse electromagnetic radiation according to wavelength; directing wavelength components of the radiation dispersed by the apparatus to the array of detectors or optical channels; and linearly interpolating the wavelength components to obtain information for calibrating the apparatus.
 33. The method of claim 32, wherein said directing directs wavelength components of the radiation dispersed by the apparatus to a two dimensional detector array or optical channels.
 34. The method of claim 33, further comprising detecting wavelength components of the radiation dispersed by the apparatus by means of a two dimensional detector array comprising a plurality of groups of detectors, each group detecting electromagnetic radiation of a corresponding wavelength range in a spectrum, and wherein said interpolating interpolates outputs of groups of detectors of the array.
 35. The method of claim 33, further comprising aligning the array with the dispersed radiation.
 36. An apparatus for determining optical characteristics of radiation, comprising: at least a first and a second element that disperse electromagnetic radiation according to wavelength, said at least two elements having a combined dispersive characteristic such that they substantially linearly disperse the electromagnetic radiation over at least a portion of an electromagnetic spectrum, wherein said at least two elements are arranged so that the apparatus is substantially telecentric; an array of detectors detecting the electromagnetic radiation dispersed by said at least two elements; and an electronic device that linearly interpolates the detected wavelength components and adds the interpolated wavelength components of the radiation to obtain at least one optical value that characterizes the radiation.
 37. The apparatus of claim 36, said at least two elements comprising a prism integral with a lens component.
 38. The apparatus of claim 37, further comprising a lens and an aperture stop, said at least two elements comprising a grating, said aperture stop being located in an optical path between the grating and the lens, said aperture stop placed substantially at a focal point of the lens component that focuses the electromagnetic radiation from the aperture stop to the detector array.
 39. The apparatus of claim 36, further comprising an aperture stop, said at least two elements comprising a grating and a lens component, said aperture stop being located in an optical path between the grating and the lens, said aperture stop placed substantially at a focal point of the lens that focuses the electromagnetic radiation from the aperture stop to the detector array.
 40. The apparatus of claim 36, further comprising a lens, said at least two elements including a prism and a grating, wherein the prism, lens and grating are separate components.
 41. The apparatus of claim 36, further comprising a lens, said at least two elements including a prism and a grating, wherein any two or more of the prism, lens and grating are combined to form a unitary single optical component.
 42. The apparatus of claim 41, wherein the prism, lens and grating form a unitary single optical component.
 43. The apparatus of claim 36, said at least two elements including a prism, a grating and a lens component integral with the prism. 